Pressure vessels are a vast and diverse field spanning from tiddly-wink instrument air receivers to cryogenic propellant tanks and beyond. There is no one size fits all approach since technical requirements are vastly different for each application.

Zeroth law, it must meet customer technical requirements and the code. Dont use FCAW when ultra pure TIG is required for sanitary systems. First, it should be done with all the proper procedure and personnel qualifications. Second, it should be economical. Don't specify electron beam welding when your competitor is using MIG for the same tank. Don't stick weld when your competitor is using SAW. Etc etc

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Not making a decision is a decision in itself

Assuming we're talking about ASME vessels in Section VIII, and welding to Section IX.

The weld process is part of the Weld Procedure Specification (WPS), which defines the values of your essential variables and does not allow them to change.

You can only use qualified (meaning demonstrated to the code's requirements) processes on code work, welded by qualified welders. So your limitations exist within the capabilities of your resources - welders and engineers.

If you can write a WPS, demonstrate its suitability, and qualify your welders/equipment as capable of meeting the WPS - you can pretty much use any method or material as you see fit. You will need to justify anything too abnormal, but the rule of thumb is that everything is permitted unless specifically mentioned in the code. They're not telling you HOW to build your vessel, they're telling you how to make sure you're doing so safely with the correct analysis and quality control required of what is a safety issue.